New soliton solutions of the conformable time fractional Drinfel'd–Sokolov–Wilson equation based on the complete discriminant system method by Shi Da, Li Zhao

“…After fractional order travelling transformation, the partial differential equation studied in this article is transformed into ordinary differential equation and connected with a quadratic polynomial. …”
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On the solution of two-dimensional local fractional LWR model of fractal vehicular traffic flow by Pranay Goswami, Bhawna Pokhriyal, Kranti Kumar

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New insights into fractional twin-core couplers: bifurcation and sensitivity analysis by Zizhao Zhou, M. S. Abbas, K. El-Rashidy, Intakhab Alam Qadri, Muhammad Abuzar, Ali Akgül, Murad Khan Hassani

“…Abstract This paper analyses the analytical solutions of the fractional twin-core coupler (fTCC) equations, which include Kerr law nonlinearity, utilising the unified and sub-ODE methods along with beta and M-truncated fractional derivatives. …”
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Gas well productivity prediction based on fractional Fourier transform by Chenchang Zheng, Jun Tang, Mengfan Li, Gewei Qi

“…In order to solve this problem, this paper uses relatively low cost logging data to investigate the relationship between Stoneley wave, longitudinal and transverse wave sign and reservoir characteristics. Fractional Fourier transform is introduced to improve signal processing methods and extract key parameters, including Stoneley wave frequency offset rate and energy attenuation coefficient of longitudinal and transverse wave. …”
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An Approximate Analytical View of Fractional Physical Models in the Frame of the Caputo Operator by Mashael M. AlBaidani, Abdul Hamid Ganie, Adnan Khan, Fahad Aljuaydi

“…Additionally, we compare our results with the Laplace residual power series method (LRPSM), the natural transform decomposition method (NTDM), and the homotopy analysis shehu transform method (HASTM). …”
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Analytical solutions of the time-fractional symmetric regularized long wave equation using the $$\phi ^{6}$$ model expansion method by Khaled Aldwoah, Nidal Eljaneid, Bakri Younis, Mohammed Alsharafi, Osman Osman, Blgys Muflh

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W transform and its application in fractional linear systems with rational powers by Guishu Liang, Mingjue Jiang

“…When this transformation is applied to fractional linear systems with rational powers, the expansion formula will have a large number of terms if the traditional decomposition method is used, which makes the form of time‐domain solutions more complex. …”
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Optical soliton solutions, dynamical and sensitivity analysis for fractional perturbed Gerdjikov–Ivanov equation by Muhammad Shakeel, Fehaid Salem Alshammari, Hameed Gul Ahmadzai

“…For this purpose, a wave transformation is applied to convert the fractional PGI Equation to a non-linear ODE. …”
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Analytical Solutions for the Equal Width Equations Containing Generalized Fractional Derivative Using the Efficient Combined Method by Mohammadhossein Derakhshan

“…In this paper, the efficient combined method based on the homotopy perturbation Sadik transform method  (HPSTM) is applied to solve the physical and functional equations containing the Caputo–Prabhakar fractional derivative. …”
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A new method to solve multi-objective linear fractional programming problem in fuzzy stochastic environment by Ajeet Kumar, Babita Mishra

“…The chance-constrained programming method is utilized to transform the MOFSLFPP into its equivalent crisp form. …”
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Exploring the dynamics of multiplicative noise on the fractional stochastic Fokas-Lenells equation by Ali R. Ansari, Adil Jhangeer, Beenish, Mudassar Imran, Abdallah M. Talafha

“…The new extended direct algebraic method is applied to construct various types of fractional solutions, including trigonometric, complex, hyperbolic, and exponential forms. …”
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Applications of the Novel (G′/G)-Expansion Method for a Time Fractional Simplified Modified Camassa-Holm (MCH) Equation by Muhammad Shakeel, Qazi Mahmood Ul-Hassan, Jamshad Ahmad

“…A generalized fractional complex transform is properly used to convert this equation to ordinary differential equation and, as a result, many exact analytical solutions are obtained with more free parameters. …”
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An Enhanced Phase Gradient Autofocus Algorithm for SAR: A Fractional Fourier Transform Approach by Kanghyuk Seo, Yonghwi Kwon, Chul Ki Kim

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A fractional-order differential equation model of diabetes mellitus type by Shikha Dadhich, Mahaveer Prasad Yadav, Kritika

“…Here, a numerical algorithm based on Fractional Homotopy Analysis Transform Method (FHATM) is constituted to study the fractional form of the model for Diabetes Mellitus Type [Formula: see text]. …”
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Robust Fractional Low Order Adaptive Linear Chirplet Transform and Its Application to Fault Analysis by Junbo Long, Changshou Deng, Haibin Wang, Youxue Zhou

“…Based on the insensitive property of fractional low-order statistics for infinite variance and Gaussian processes, robust fractional lower order adaptive linear chirplet transform (FLOACT) and fractional lower order adaptive scaling chirplet transform (FLOASCT) methods are proposed to suppress the mixed complex noise in this paper. …”
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A vitamin intervention study on the tumour and immune cells via TIV dynamical system-revisited by Khushbu Agrawal, Sunil Kumar, Badr Saad T. Alkahtani, Sara Salem Alzaid

“…For the first time, fractional order TIV system has been solved by using Bernstein wavelet collocation method (BWCM). …”
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Caputo fractional derivative in the solution of Kolmogorov equations: a new numerical approach by Mohammad Alshammari, Saleh Alshammari, Manoj Singh, Yousef Jawarneh, Nedal M. Mohammed, Khalid M. K. Alshammari

“…This paper explores the application of the Caputo fractional derivative in solving FOPDEs and systems, presenting a novel numerical method that combines the Laplace transform with the Least-Squares Residual Power-Series Method. …”
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On Analytical Solution of Time-Fractional Biological Population Model by means of Generalized Integral Transform with Their Uniqueness and Convergence Analysis by Saima Rashid, Rehana Ashraf, Ebenezer Bonyah

“…To investigate the closed form solutions, we employed a fractional complex transform to deal with a partial differential equation of fractional order and a generalized decomposition method was applied to analyze the nonlinear equation. …”
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Influence of the $ \beta $-fractional derivative on optical soliton solutions of the pure-quartic nonlinear Schrödinger equation with weak nonlocality by Mahmoud Soliman, Hamdy M. Ahmed, Niveen Badra, M. Elsaid Ramadan, Islam Samir, Soliman Alkhatib

“…Graphical illustrations clearly depict these transformations, highlighting how fractional derivatives have a major impact on the properties of solitons. …”
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On the Extended Simple Equations Method (SEsM) for Obtaining Numerous Exact Solutions to Fractional Partial Differential Equations: A Generalized Algorithm and Several Applications by Elena V. Nikolova

“…In this article, we present the extended simple equations method (SEsM) for finding exact solutions to systems of fractional nonlinear partial differential equations (FNPDEs). …”
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